Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
984 conjugacy classes of subgroups; only the 226 normal subgroups are shown.
This group has 984 conjugacy classes of subgroups — too many to draw. Only its 226 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C25×C13 | D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C24×C4×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C13×#2076 | C2 | semidirect |
| 3. C13×#2036 | C2 | semidirect |
| 4. C13×#2001 | C2 | semidirect |
| 7. C22×C13×Q16 | C22 | semidirect |
| 9. C2×C13×#107 | C22 | semidirect |
| 10. C2×C13×#103 | C22 | semidirect |
| 16. C13×#340 | C22 | semidirect |
| 17. C13×#340 | C22 | semidirect |
| 38. #32710 | C13 | direct (N × H) |
| 41. C24×C13 | Q16 | semidirect |
| 67. #2076 | C2×C13 | semidirect |
| 68. #2036 | C2×C13 | semidirect |
| 69. #2001 | C2×C13 | semidirect |
| 96. C22×Q16 | C22×C13 | semidirect |
| 98. C2×#107 | C22×C13 | semidirect |
| 99. C2×#103 | C22×C13 | semidirect |
| 105. #340 | C22×C13 | semidirect |
| 106. #340 | C22×C13 | semidirect |
| 147. C24 | C13×Q16 | semidirect |
| 172. C13 | #32710 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#2848 | 2 |
| C13×#2076 | 2 |
| C13×#2036 | 2 |
| C13×#2001 | 2 |
| C13×#1779 | 2 |
| #32710 | 13 |